Now, consider the question:
At what point in time is the particle at rest?
The obvious answer is at 20 seconds, but I'm having trouble visualizing exactly why. One could say "The particle is not moving at 20 seconds, therefore it is at rest." But couldn't you say the same thing about any other point on this graph? If you froze time at 18 seconds, the particle would not be moving. "Yes, but if you unfreeze time, it is clearly moving." Again, same thing at 20 seconds. The particle isn't moving after 20 seconds, but only instantaneously. At 20.000000...1 seconds, the particle does move, so the only way to find evidence of the object's "rest" is to freeze time and watch it not move. But then again, you can freeze time at any point and the object will not move. So what is rest? The absence of movement? Or just the absence of velocity?
Apologies if this seems like an extremely stupid question.